Thu, 28 May 2026
16:00
Lecture Room 4

AI-driven discovery in number theory & beyond

Yang-Hui He
(London Institute for Mathematical Sciences)
Abstract
We argue how AI can assist mathematics in three ways: theorem-proving, conjecture formulation, and language processing.
 
Inspired by initial experiments in geometry and string theory in 2017, we summarize how this emerging field has grown over the past years, and show how various machine-learning algorithms can help with pattern detection across disciplines ranging from algebraic geometry to representation theory, to combinatorics, and to number theory. 
 
At the heart of the programme is the question how does AI help with theoretical discovery, and the implications for the future of mathematics.
Thu, 14 May 2026
16:00
Lecture Room 4

A structure theorem for sets with doubling 4 + $\delta$

Akshat Mudgal
(University of Warwick )
Abstract

A question of Ben Green asks whether every finite set $A$ of integers with doubling constant $K$ must contain a subset $A'$ of comparable size whose doubling is at most $K + o(1)$ due to some explicit algebraic structure on $A'$. This was previously understood in the regime $K < 4 - o(1)$ by work of Eberhard, Green, and Manners, who showed that one can find such a subset $A'$ with density at least $1/2 + o(1)$ inside a long arithmetic progression. In this talk, I will provide a brief survey of this question as well as mention some new progress towards this. This is joint work with Yifan Jing.

A comparison of bias approximations for the 2SLS estimator
 Bun, M Windmeijer, F
Waiting lists, waiting times and admissions: an empirical analysis at hospital and general practice level
 Gravelle, H Hoonhout, P Windmeijer, F
Genetic markers as instrumental variables: an application to child fat mass and academic achievement
 Davey Smith, G von Hinke, S Lawlor, D Propper, C Windmeijer, F
Endogeneity in count data models; an application to demand for health care
 Santos Silva, J Windmeijer, F
Two-part multiple spell models for health care demand
 Santos Silva, J Windmeijer, F
Estimating structural mean models with multiple instrumental variables using the generalised method of moments
 Clarke, P Palmer, T Windmeijer, F
Is it different for zeros? Discriminating between models for non-negative data with many zeros
 Santos Silva, J Tenreyro, S Windmeijer, F
The weak instrument problem of the system GMM estimator in dynamic panel data models
 Bun, M Windmeijer, F
Subscribe to